Determine collinear PDFs beyond twist three

Determine the collinear parton distribution functions beyond geometrical twist three that are required to extend the twist decomposition of gluon TMD correlators to higher-twist contributions.

Background

The paper explains that the twist decomposition of the small-b expansion of gluon TMD correlators is generally truncated at geometrical twist three. This truncation prevents the systematic inclusion of higher-twist matching contributions because the relevant collinear parton distribution functions are not presently known. Knowledge of these distributions would enable higher-twist extensions of the tree-level matching relations, including contributions relevant to distributions such as pretzelosity, which the paper states are expected to match onto twist-four and twist-five collinear PDFs.

References

At the current stage, the twist decomposition is usually truncated at the geometrical twist 3 components, as collinear PDFs beyond twist 3 are essentially unknown and, in any case, not relevant for current phenomenology.

— Matching relations for gluon TMDs up to one-loop accuracy  (2609.16945 - Alvaro et al., 15 Sep 2026) in Section 2, "Tree-level computation"